Restoration of localized damaged areas (time signals, but guess also applicable to images)
So , you want to remove the "noise" (damaged signal) from the signal, by giving the perfect signal as output. This model is called as a "denoising autoencoder". If you have enough training data, the noise is not at all a problem for the neural network , if you really feel that the network is capturing the noise , then you have to increase the training epochs , or sometimes it can be a bad initialized network.